trying to prove that the sum of consecutive odd numbers is always the difference of two sqaures.

First I listed the odd numbers

1; 3; 5; 7; 9,

Then difference of two squares

4 -1 = 3

9-4 = 5

16 - 4 = 12 = 5 +7 (sum of odd numbers)

25 - 4 = 21 = 5 + 7 + 9

How do I generalise? please help.

Your prompt says you are "trying to prove that the sum of consecutive odd numbers is always the difference of two sqaures." However, what you are actually trying to prove is that the difference of two squares is the sum of consecutive odd numbers. I just want it to be clear you have this written backwards.

To "prove" the sum of consecutive odd numbers is always a difference of two squares, you would have to show that:
(2n + 1) + (2n + 3) = a^2 - b^2

is true for any value of n = 0, 1, 2,..., where a and b are integer numbers. But this isn't true.